Rogue waves and hybrid solutions of the Davey–Stewartson I equation

Explicit forms of rogue waves and hybrid solutions of the Davey–Stewartson I (DS I) equation are derived by performing an appropriate limiting procedure on soliton solutions that are generated by the Hirota bilinear method. Using this method, many interesting, from the physical point of view, hybrid...

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Bibliographic Details
Published inNonlinear dynamics Vol. 95; no. 1; pp. 839 - 857
Main Authors Liu, Yaobin, Qian, Chao, Mihalache, Dumitru, He, Jingsong
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2019
Springer Nature B.V
Subjects
Automotive Engineering
Automotive parts
Classical Mechanics
Control
Dynamical Systems
Engineering
Exact solutions
Lie groups
Mechanical Engineering
Original Paper
Partial differential equations
Physics
Solitary waves
Vibration
Davey–Stewartson I equation
Rogue waves
Hybrid solutions
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Summary:Explicit forms of rogue waves and hybrid solutions of the Davey–Stewartson I (DS I) equation are derived by performing an appropriate limiting procedure on soliton solutions that are generated by the Hirota bilinear method. Using this method, many interesting, from the physical point of view, hybrid solutions are constructed. The hybrid solutions illustrate various superimposed wave structures involving rogue waves, lumps, solitons, and periodic line waves. The unique ( 2 + 1 )-dimensional dynamics of the obtained exact solutions of the DS I equation may help to understand the formation and key properties of rogue waves in many other physical settings.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4599-x